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401-3308-24L 4 Credits BSC , MSC D-MATH

Riemann Surfaces

Lecturers & Examiners: Dr. Alessandro Giacchetto
VVZ CR n/a

Last Updated: 2026-02-05 16:37:24

Abstract

The course will be a first introduction to Riemann surfaces. These are beautiful objects that sit at the intersection of algebra, geometry, and analysis. We will aim to cover the theorems of Riemann–Hurwitz and Riemann–Roch, as well as the basics of Hurwitz theory. Time permitting, we may delve into additional subjects such as abelian integrals and the Abel–Jacobi theorem.

Objective

The topics presented in the course will include: * Basic facts about Complex Analysis and Manifold Theory * Topology of Riemann surfaces * Meromorphic functions and divisors * Riemann–Roch theorem * Hurwitz theory

Resources

Literature

* E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris. Geometry of Algebraic Curves, Volume 1. Springer-Verlag, 1985 * R. Cavalieri, E. Miles. Riemann Surfaces and Algebraic Curves. Cambridge University Press, 2016 * O. Forster. Lectures on Riemann Surfaces. Springer-Verlag, 1981

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
session examination
Mode
oral 20 minutes
The exam is offered only in the Summer 2024, Winter 2025, Summer 2025 and Winter 2026 examination sessions.

Course Components

Type Title Time & Place Hours
lecture Riemann Surfaces
  • Thu 16:15-18:00 (HG D 5.2)
2 h weekly

Offered In